Somehow I feel this question is backwards. It should be "does your pet allow You to sleep on the bed with them?" Sometimes convincing Rascal he must share the bed is a challenge.

I have so many fond memories of Mr. Magic (Rainbow Bridge). He was a stray that insisted he was going to live with me. It didn't take much to convince me. the very first night that I put him on the bed, he was tentative about it. But when I turned out the light he was frightened. My guess is that he had always been an outdoor stray and if you think about it, the sun doesn't just "go out". I quickly turned the light back on and reassured him. That only made me love him more.